String Effects in the Wilson Loop: a high precision numerical test

TL;DR

The paper tests the hypothesis that confinement in lattice gauge theories is described by an effective string in the infrared, using the exactly solvable 3d $ ext{Z}_2$ gauge model. By constructing parameter-free ratios of Wilson loops, the authors compare high-precision Monte Carlo data to the bosonic-string prediction $\langle W(R,T)\rangle = e^{-\sigma RT+p(R+T)+k} [\eta( au)/\sqrt{R}]^{-(d-2)/2}$ with $\tau=iT/R$, thereby extracting the universal flux-tube fluctuation effects. The results show that the entire finite-size correction, captured by the Dedekind eta function factor, matches the data with reduced $\chi^2\approx1.2$, while the simpler conformal-anomaly term alone fails, highlighting the importance of the full string partition function in the infrared. The work supports universality of the effective string description across confining LGTs and demonstrates that large Wilson-loop data are essential to unambiguously identify the correct effective string theory, with implications for broader classes of gauge theories and interfaces. $

Abstract

We test numerically the effective string description of the infrared limit of lattice gauge theories in the confining regime. We consider the 3d Z(2) lattice gauge theory, and we define ratios of Wilson loops such that the predictions of the effective string theory do not contain any adjustable parameters. In this way we are able to obtain a degree of accuracy high enough to show unambiguously that the flux--tube fluctuations are described, in the infrared limit, by an effective bosonic string theory.

Figures (2)

• Figure 1: Comparison of the prediction of the free string model with Monte Carlo data for the ratios $R(L,n)$. The solid line is the prediction of the string model, Eq. (\ref{['ft']}). The dotted line is the same prediction when only the conformal anomaly term is taken into account, Eq. (\ref{['f0']}).
• Figure 2: Finite--size effects for small Wilson loop. The prediction of the free string model is $R(L,L/2)=1.09153\dots$ (straight line).